1 // This file is part of Eigen, a lightweight C++ template library
2 // for linear algebra.
3 //
4 // Copyright (C) 2010,2012 Jitse Niesen <jitse@maths.leeds.ac.uk>
5 //
6 // This Source Code Form is subject to the terms of the Mozilla
7 // Public License v. 2.0. If a copy of the MPL was not distributed
8 // with this file, You can obtain one at http://mozilla.org/MPL/2.0/.
9
10 #include "main.h"
11 #include <limits>
12 #include <Eigen/Eigenvalues>
13
verifyIsQuasiTriangular(const MatrixType & T)14 template<typename MatrixType> void verifyIsQuasiTriangular(const MatrixType& T)
15 {
16 typedef typename MatrixType::Index Index;
17
18 const Index size = T.cols();
19 typedef typename MatrixType::Scalar Scalar;
20
21 // Check T is lower Hessenberg
22 for(int row = 2; row < size; ++row) {
23 for(int col = 0; col < row - 1; ++col) {
24 VERIFY(T(row,col) == Scalar(0));
25 }
26 }
27
28 // Check that any non-zero on the subdiagonal is followed by a zero and is
29 // part of a 2x2 diagonal block with imaginary eigenvalues.
30 for(int row = 1; row < size; ++row) {
31 if (T(row,row-1) != Scalar(0)) {
32 VERIFY(row == size-1 || T(row+1,row) == 0);
33 Scalar tr = T(row-1,row-1) + T(row,row);
34 Scalar det = T(row-1,row-1) * T(row,row) - T(row-1,row) * T(row,row-1);
35 VERIFY(4 * det > tr * tr);
36 }
37 }
38 }
39
schur(int size=MatrixType::ColsAtCompileTime)40 template<typename MatrixType> void schur(int size = MatrixType::ColsAtCompileTime)
41 {
42 // Test basic functionality: T is quasi-triangular and A = U T U*
43 for(int counter = 0; counter < g_repeat; ++counter) {
44 MatrixType A = MatrixType::Random(size, size);
45 RealSchur<MatrixType> schurOfA(A);
46 VERIFY_IS_EQUAL(schurOfA.info(), Success);
47 MatrixType U = schurOfA.matrixU();
48 MatrixType T = schurOfA.matrixT();
49 verifyIsQuasiTriangular(T);
50 VERIFY_IS_APPROX(A, U * T * U.transpose());
51 }
52
53 // Test asserts when not initialized
54 RealSchur<MatrixType> rsUninitialized;
55 VERIFY_RAISES_ASSERT(rsUninitialized.matrixT());
56 VERIFY_RAISES_ASSERT(rsUninitialized.matrixU());
57 VERIFY_RAISES_ASSERT(rsUninitialized.info());
58
59 // Test whether compute() and constructor returns same result
60 MatrixType A = MatrixType::Random(size, size);
61 RealSchur<MatrixType> rs1;
62 rs1.compute(A);
63 RealSchur<MatrixType> rs2(A);
64 VERIFY_IS_EQUAL(rs1.info(), Success);
65 VERIFY_IS_EQUAL(rs2.info(), Success);
66 VERIFY_IS_EQUAL(rs1.matrixT(), rs2.matrixT());
67 VERIFY_IS_EQUAL(rs1.matrixU(), rs2.matrixU());
68
69 // Test maximum number of iterations
70 RealSchur<MatrixType> rs3;
71 rs3.setMaxIterations(RealSchur<MatrixType>::m_maxIterationsPerRow * size).compute(A);
72 VERIFY_IS_EQUAL(rs3.info(), Success);
73 VERIFY_IS_EQUAL(rs3.matrixT(), rs1.matrixT());
74 VERIFY_IS_EQUAL(rs3.matrixU(), rs1.matrixU());
75 if (size > 2) {
76 rs3.setMaxIterations(1).compute(A);
77 VERIFY_IS_EQUAL(rs3.info(), NoConvergence);
78 VERIFY_IS_EQUAL(rs3.getMaxIterations(), 1);
79 }
80
81 MatrixType Atriangular = A;
82 Atriangular.template triangularView<StrictlyLower>().setZero();
83 rs3.setMaxIterations(1).compute(Atriangular); // triangular matrices do not need any iterations
84 VERIFY_IS_EQUAL(rs3.info(), Success);
85 VERIFY_IS_APPROX(rs3.matrixT(), Atriangular); // approx because of scaling...
86 VERIFY_IS_EQUAL(rs3.matrixU(), MatrixType::Identity(size, size));
87
88 // Test computation of only T, not U
89 RealSchur<MatrixType> rsOnlyT(A, false);
90 VERIFY_IS_EQUAL(rsOnlyT.info(), Success);
91 VERIFY_IS_EQUAL(rs1.matrixT(), rsOnlyT.matrixT());
92 VERIFY_RAISES_ASSERT(rsOnlyT.matrixU());
93
94 if (size > 2 && size < 20)
95 {
96 // Test matrix with NaN
97 A(0,0) = std::numeric_limits<typename MatrixType::Scalar>::quiet_NaN();
98 RealSchur<MatrixType> rsNaN(A);
99 VERIFY_IS_EQUAL(rsNaN.info(), NoConvergence);
100 }
101 }
102
test_schur_real()103 void test_schur_real()
104 {
105 CALL_SUBTEST_1(( schur<Matrix4f>() ));
106 CALL_SUBTEST_2(( schur<MatrixXd>(internal::random<int>(1,EIGEN_TEST_MAX_SIZE/4)) ));
107 CALL_SUBTEST_3(( schur<Matrix<float, 1, 1> >() ));
108 CALL_SUBTEST_4(( schur<Matrix<double, 3, 3, Eigen::RowMajor> >() ));
109
110 // Test problem size constructors
111 CALL_SUBTEST_5(RealSchur<MatrixXf>(10));
112 }
113